Your speakers are generally well regarded. Any decent integrated amp should work well pending a device to accept your digital input. Those Polks are fairly efficient and should be happy with at least 100 watts per channel unless you have a huge room. AudiogoN is a great place to find value in high end equipment.

I would look at a decent DAC to run the optical digital output of your ATV into and then run the RCA outputs from the DAC to your selected integrated amp or preamp/poweramp. The DIYEDEN Great March 2 is a great DAC for $400.

If you are going to stay with two channel then a DAC and integrated amps or a preamp/poweramp would be in order. If you want to be able to upgrade to 5.1 ot 7.1 in the future then some kind of AV receiver or preprocessor/poweramp (they have a built in DAC) would be required. I've heard that some music titles (SACD and DVD-A) sound really good on a multichannel system and of course movies are mixed with surround sound. However, I don't know if the majority of your listening will be lossless digital files or not. I also don't know if digital music files are available in a multichannel format. Multichannel sources can always be downmixed to two channel with no problems. I personally would not make my music system multichannel and would stay with two channel unless I was going to watch movies with it as well.

I guess you need to decide if this will be a dedicated music system where two channel would suffice or you will need multichannel capability for movies and potential multichannel digital sources.

There are preprocessors and receivers that have an HT bypass so that they can be used as a two channel system for critical listening of music or as a 5.1/7.1 system for movies and other multichannel material.

A multichannel preprocessor with HT bypass and one two channel power amplifier could be the base of your system, allowing stereo listening now and an upgrade to multichannel later when you get more power amplifiers and loudspeakers for the remaining three or five channels.

The replacement for the Emotiva MMC-1 is due at the end of the year. Paired with an XPA-2 power amplifier you would have the beginnings of your system. Emotiva makes the XPA-3 which is a 200 watt per channel three channel amp that could be added later when you get a center and surrounds. http://emotiva.com/about/products.html

Outlaw makes some reasonably priced gear as well. The Outlaw Model 990 preprocessor and a pair of Outlaw M-2200 M-Blocks for $1400 would be another start. Then you could get three more M-2200s for $1050 to round out a 5.1. http://emotiva.com/about/products.html

The NAD M15 preprocessor ($3000) and perhaps NAD C272 power amp ($600) could be another start.

In all of this multichannel discussion you would also consider if you needed a subwoofer. The Polk RTi/A9s will do fine with music material but would be lacking in some of the sub-30Hz material you find in movies.

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I have a hifi system but classical music just doesn't do very well on that at all...

It can't be all that "hifi" if it doesn't do well with your classical music. I think your Polk RTi A9s driven by the Emotiva stuff would be a vast improvement.

If and when you go multichannel you should consider matching your Polk RTi A9 mains with a Polk CSi A6 center ($350) and a pair of Polk RTi A3s ($400) for 5.1 or a pair of Polk FXi A6s ($500) for 7.1.

For a subwoofer you can't do much better than the SVS PB13-Ultra for $1600. It integrates well with most systems, is musical, and will handle all movies can throw at it. http://www.svsound.com/products-sub-box-pb13ultra.cfm